Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	33	17
1	114	17
2	563	17
3	4164	17
4	5002	17

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

2.9b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

319.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

464.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

272.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series387.0ms

Counts

3 → 9

Calls

3 calls:

144.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

160.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

83.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify130.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1439	12925
1	5002	12452

prune925.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite914.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac`
160×	`*-un-lft-identity`
120×	`add-sqr-sqrt` `sqrt-prod`
108×	`add-cube-cbrt`
26×	`distribute-lft-out`
20×	`associate-/r/`
12×	`flip3-+` `flip-+`
10×	`div-inv`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
6×	`pow1` `rem-sqrt-square` `associate-/r*`
4×	`associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

4 → 216

Calls

4 calls:

179.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
179.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
271.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
273.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series554.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
195.0ms	(sqrt (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
80.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	629	4786
1	2301	4502
2	5003	4350

prune910.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
0.0b	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0)))
1.7b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
2.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

4788×	`times-frac`
2658×	`*-un-lft-identity`
1682×	`add-sqr-sqrt` `add-cube-cbrt`
488×	`distribute-lft-out`
365×	`associate-/r/`
361×	`difference-of-squares`
183×	`div-inv`
104×	`associate-/l*`
100×	`flip3--` `flip--`
84×	`flip3-+` `flip-+`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r*`
20×	`cbrt-undiv` `div-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 1705

Calls

4 calls:

564.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
277.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0)))
332.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
278.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0))))
52.0ms	(/ (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (- (+ alpha beta) (* 2.0 1.0)))
167.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))
86.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify604.0ms

Algorithm

egg-herbie

Counts

1717 → 1717

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5001	80332

prune4.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.0b	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
18.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

251×	`times-frac`
206×	`*-un-lft-identity`
147×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
66×	`associate-r`
40×	`distribute-lft-out`
34×	`add-exp-log` `add-cbrt-cube`
28×	`associate-/r/`
22×	`associate-l` `associate-/l*`
14×	`cbrt-undiv` `div-exp` `div-inv`
13×	`flip3-+` `flip-+`
11×	`associate-/r*`
9×	`difference-of-squares`
6×	`pow1` `prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`associate-/l/`
4×	`add-log-exp`
3×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 287

Calls

4 calls:

210.0ms	(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
90.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
772.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
280.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

series475.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
48.0ms	(/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0)))
224.0ms	(* (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0)))) (/ (/ (- (+ alpha beta) (* 2.0 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
126.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (- (* (+ alpha beta) (+ alpha beta)) (* (* 2.0 1.0) (* 2.0 1.0))))

simplify87.0ms

Algorithm

egg-herbie

Counts

299 → 299

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1273	6877
1	5001	6381

prune806.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 1.1b

regimes51.0ms

Accuracy

53.8% (1.2b remaining)

Error of 2.4b against oracle of 1.2b and baseline of 3.8b

bsearch60.0ms

Steps

Iters	Range		Point
7	1.4322694484134952e+160	2.8602589239887756e+162	3.96094467204414e+160

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	53
1	43	53

end0.0ms

sample570.0ms

Algorithm

intervals

Results

290.0ms	8000×	body	80	valid
96.0ms	8000×	pre	80	true